Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class FunkyNumbers192A {
	
	static ArrayList<Long>  numerosTriangulares = new ArrayList<Long>();
	
	public static void main(String [] args){
		numeros();
		Scanner entrada = new Scanner(System.in);
		long n= entrada.nextLong();
		boolean estado=false;
		int size=numerosTriangulares.size();
		for(int i=0;i<size;i++){
			long d=n-numerosTriangulares.get(i);
			if(busqueda(d)!=-1){
				System.out.println("YES");
				System.exit(0);
			}
		}
		System.out.println("NO");
	}
	
	public static int busqueda(long i){
		int superior=numerosTriangulares.size()-1, inferior=0;
		int b=-1;
		
		while(inferior<=superior){
			int centro = (superior+inferior)/2;
			if(numerosTriangulares.get(centro)==i){
				b=centro;
				break;
			}else if(numerosTriangulares.get(centro)>i){
					superior=centro-1;					
				}else{
					inferior=centro+1;					
				}
		}
		
		return b;
	}
	
	public static void numeros(){
		long g=1000000000, f = 0;
		for(int i=1;f<=g;i++){
			f=Long.valueOf((i*(i+1))/2);
			numerosTriangulares.add(f);
		}
		Collections.sort(numerosTriangulares);
	}
}